Theory for externally contracted configuration interaction energy gradients

A derivation of the analytic energy gradient based upon a multireference externally contracted configuration interaction (MRCCI) wave function is presented. Computational efficiency was the major consideration in deciding upon the approach chosen. The final set of equations which define the gradient are computationally efficient, and avoid writing to disk or transforming any derivative integrals. It is also shown that the MRCCI gradient, evaluated in this way, does not require solving any coupled-perturbed configuration interaction (CPCI) equations. Thus, the formulation presented here demonstrates that the MRCCI gradient is much less expensive than the uncontracted multireference CI (MCSCF-CI) energy gradient. A general set of equations for an internally contracted CI energy gradient is also presented.